粘弹性流体流经作依赖时间运动伸展面的三维流动及其传质问题

T·哈亚特; M·穆斯塔法

doi:10.3879/j.issn.1000-0887.2011.02.004

粘弹性流体流经作依赖时间运动伸展面的三维流动及其传质问题

doi: 10.3879/j.issn.1000-0887.2011.02.004

T·哈亚特^1,2,
M·穆斯塔法¹

奎得衣阿扎姆大学力学系,伊斯兰堡 44000, 巴基斯坦;

详细信息

中图分类号: O361
计量
- 文章访问数: 1467
- HTML全文浏览量: 180
- PDF下载量: 732
- 被引次数: 0
出版历程
- 收稿日期: 2010-07-02
- 修回日期: 2010-10-29
- 刊出日期: 2011-02-15

Time-Dependent Three-Dimensional Flow and Mass Transfer of an Elastico-Viscous Fluid Over an Unsteady Stretching Sheet

T. Hayat^1,2,
M. Mustafa¹

Department of Mathematics, Quaid-I-Azam University 45320, Islamabad 44000, Pakistan;
Department of Mathematics, College of Science, King Saud University, P. O. Box 2455, Riyadh 11451, Saudia Arabia

摘要

摘要: 研究粘弹性流体流经伸展面时的三维边界层流动．假定伸展面的运动速度依赖于时间．进一步考虑了更高阶次化学反应对传质的影响．应用同伦分析法(HAM)进行计算．精确地分析了所得级数解的收敛性．用图形讨论了各参数变化对速度和浓度的影响．还给出了面传质数值的计算，将所得结果与前人的数值解进行了比较．
- 不稳定流动 /
- 传质 /
- 粘弹性流体 /
- HAM解
Abstract: The three-dimensional boundary layer flow of an elastico-viscous fluid over a stretching surface was looked at. Velocity of the stretching sheet was assumed to be time-dependent. Effect of mass transfer with higher order chemical reaction was further considered. Computations were made by homptopy analysis method(HAM). The convergence of the obtained series solutions was explicitly analyzed. The variations of embedding parameters on the velocity and concentration were graphically discussed. Numerical computations of surface mass transfer were reported. Comparison of the present results with the numerical solutions was also seen.
- unsteady flow /
- mass transfer /
- viscoelastic fluid /
- HAM solution

HTML全文

参考文献(34)

[1]	Fetecau C, Fetecau C. Starting solutions for some unsteady unidirectional flows of a second grade fluid[J]. International Journal of Engineering Science, 2005, 43(10): 781-789. doi: 10.1016/j.ijengsci.2004.12.009
[2]	Fetecau C, Athar M, Fetecau C. Unsteady flow of a generalized Maxwell fluid with fractional derivative due to a constantly accelerating plate[J]. Computers and Mathematics With Applications, 2008, 57(4): 596-603.
[3]	Fetecau C, Fetecau Corina. Starting solutions for the motion of a second grade fluid due to longitudnal and torsional oscillations of a circular cylinder[J]. International Journal of Engineering Science, 2006, 44(11/12): 788-796. doi: 10.1016/j.ijengsci.2006.04.010
[4]	Tan W C, Xiao P W, Yu X M. A note on unsteady flows of a viscoelastic fluid with the fractional Maxwell model[J]. International Journal of Nonlinear Mechanics, 2003, 38(5): 645-650. doi: 10.1016/S0020-7462(01)00121-4
[5]	Hayat T, Ahmad N, Ali N. Effects of endoscope and magnetic field on the peristalsis involving Jeffrey fluid[J]. Communications in Nonlinear Science and Numerical Simulation, 2008, 13(8): 1581-1591. doi: 10.1016/j.cnsns.2007.02.008
[6]	Hayat T, Mustafa M, Asghar S. Unsteady flow with heat and mass transfer of a third grade fluid over a stretching surface in presence of chemical reaction[J]. Nonlinear Analysis: Real World Applications, 2010, 11(4): 3186-3197. doi: 10.1016/j.nonrwa.2009.11.012
[7]	Hayat T, Mustafa M, Pop I. Heat and mass transfer for Soret and Dufour’s effect on mixed convection boundary layer flow over a stretching vertical surface in a porous medium filled with a viscoelastic fluid[J]. Communications in Nonlinear Science and Numerical Simulation, 2010, 15(5): 1183-1196. doi: 10.1016/j.cnsns.2009.05.062
[8]	Devi C D S, Takhar H S, Nath G. Unsteady mixed convection flow in a stagnation region to adjacent to a vertical surface[J]. Heat and Mass Transfer, 1991, 26(2): 71-79.
[9]	Andersson H I, Aarseth J B, Dandapat B S. Heat transfer in a liquid film on an unsteady stretching surface[J]. International Journal of Heat and Mass Transfer, 2003, 43(1): 69-74.
[10]	Nazar R, Amin N, Pop I. Unsteady boundary layer due to a stretching surface in a rotating fluid[J]. Mechanics Research Communications, 2004, 31(1): 121-128. doi: 10.1016/j.mechrescom.2003.09.004
[11]	Elbashbeshy E M A, Bazid M A A. Heat transfer over an unsteady stretching surface[J]. Heat and Mass Transfer, 2004, 41(1): 1-4. doi: 10.1007/s00231-004-0520-x
[12]	Beard D W, Walters K. Elastico-viscous boundary layer flows I: two-dimensional flow near a stagnation point[J]. Proceedings of the Cambridge, Philosophical Society, 1964, 60(3): 667-674. doi: 10.1017/S0305004100038147
[13]	Ariel P D. Two dimensional stagnation point flow of an elastico-viscous fluid with partial slip[J]. Zeitschrift für Angewandte Mathematik und Mechanik, 2008, 88(4): 320-324. doi: 10.1002/zamm.200700041
[14]	Hayat T, Abbas Z, Pop I. Momentum and heat transfer over a continuously moving surface with a parallel free stream in a viscoelastic fluid[J]. Numerical Methods for Partial Differential Equations, 2010, 26(2): 305-319.
[15]	Cortell R. MHD flow and mass transfer of an electrically fluid of second grade in a porous medium over a stretching sheet with chemically reactive species[J]. Chemical Engineering Processing, 2007, 46(8): 721-728. doi: 10.1016/j.cep.2006.09.008
[16]	Cortell R. Towards an understanding of the motion and mass transfer with chemically reactive species for two classes of viscoelastic fluid over a porous stretching sheet[J]. Chemical Engineering Processing, 2007, 46(10): 982-989. doi: 10.1016/j.cep.2007.05.022
[17]	Nazar R, Latip N A. Numerical investigation of three-dimensional boundary layer flow due to a stretching surface in a viscoelastic fluid[J]. European Journal of Scientific Research, 2009, 29(4): 509-517.
[18]	Mukhopadhyay S. Effect of thermal radiation on unsteady mixed convection flow and heat transfer over a porous stretching surface in a porous medium[J]. International Journal of Heat and Mass Transfer, 2009, 52(13/14): 3261-3265. doi: 10.1016/j.ijheatmasstransfer.2008.12.029
[19]	Liao S J. A general approach to get series solution of non similarity boundary layer flows[J]. Communications in Nonlinear Science and Numerical Simulation, 2009, 14(5): 2144-2159. doi: 10.1016/j.cnsns.2008.06.013
[20]	Xu H, Liao S J, You X C. Analysis of nonlinear fractional partial differential equations with homotopy analysis method[J]. Communications in Nonlinear Science and Numerical Simulation, 2009, 14(4): 1152-1156. doi: 10.1016/j.cnsns.2008.04.008
[21]	Xu H, Liao S J. Dual solutions of boundary layer flow over an upstream moving plate[J]. Communications in Nonlinear Science and Numerical Simulation, 2008, 13(2): 350-358. doi: 10.1016/j.cnsns.2006.04.008
[22]	Liao S J. Notes on the homotopy analysis method: some definitions and theorems[J]. Communications in Nonlinear Science and Numerical Simulation, 2009, 14(4): 983-997. doi: 10.1016/j.cnsns.2008.04.013
[23]	Tan Y, Abbasbandy S. Homotopy analysis method for quadratic Recati differential equation[J]. Communications in Nonlinear Science and Numerical Simulation, 2008, 13(3): 539-546. doi: 10.1016/j.cnsns.2006.06.006
[24]	Abbasbandy S. The application of homotopy analysis method to solve a generalized Hirota-Satsuma coupled KdV equation[J]. Physics Letters A, 2008, 372(6): 613-618. doi: 10.1016/j.physleta.2007.07.069
[25]	Abbasbandy S, Zakaria F S. Soliton solution for the fifth-order KdV equation with homotopy analysis method[J]. Nonlinear Dynamics, 2008, 51(1/2): 83-87.
[26]	Kechil S, Hashim I. Approximate analytical solution for MHD stagnation-point flow in porous media[J]. Communications in Nonlinear Science and Numerical Simulation, 2009, 14(4): 1346-1354. doi: 10.1016/j.cnsns.2008.02.007
[27]	Hashim I, Abdulaziz O, Momani S. Homotopy analysis method for fractional IVPs[J]. Communications in Nonlinear Science and Numerical Simulation, 2009, 14(3): 674-684. doi: 10.1016/j.cnsns.2007.09.014
[28]	Hayat T, Maqbool K, Asghar S. Hall and heat transfer effects on the steady flow of a Sisko fluid[J]. Zeitschrift fur Naturforschung A, 2009, 64a(1): 769-782.
[29]	Hayat T, Maqbool K, Asghar S. The influence of Hall current and heat transfer on the flow of a fourth grade fluid[J]. Numerical Methods for Partial Differential Equations, 2010, 26(3): 501-518.
[30]	Hayat T, Qasim M, Abbas Z. Radiation and mass transfer effects on the magnetohydrodynamic unsteady flow induced by a stretching sheet[J]. Zeitschrift fur Naturforschung A, 2010, 65(1): 231 -239.
[31]	Hayat T, Qasim M, Abbas Z. Homotopy solution for the unsteady threedimensional MHD flow and mass transfer in a porous space[J]. Communications in Nonlinear Science and Numerical Simulation, 2010, 15(9): 2375-2387. doi: 10.1016/j.cnsns.2009.09.013
[32]	Hayat T, Nawaz M. Hall and ion-slip effects on three-dimensional flow of a second grade fluid[J]. International Journal for Numerical Methods in Fluids. doi: 10.1002/fld.2251.
[33]	Hayat T, Sajjad R, Asghar S. Series solution for MHD channel flow of a Jeffery fluid[J]. Communications in Nonlinear Science and Numerical Simulation, 2010, 15(9): 2400-2406. doi: 10.1016/j.cnsns.2009.09.033
[34]	Hayat T, Qasim M, Mesloub S. MHD flow and heat transfer over permeable stretching sheet with slip conditions[J]. International Journal for Numerical Methods in Fluids. doi: 10.1002/fld.2294.